1. Field of the Invention
The present invention relates to a variable capacitor used as a voltage capacity conversion device.
2. Description of the Related Art
FIG. 18 shows the configuration of a major part of a variable capacitor proposed in Japanese unexamined patent publication No. H5-74655 as an example of a variable capacitor. This variable capacitor is formed using a surface micromachining technique. In FIG. 18, a concave portion 8 is formed in a substrate 3 made of silicon, and a thin film reference electrode 4, which has been formed by means of aluminum deposition or the like, is fixed to the substrate 3 in the middle of the bottom 5 of the concave portion 8. A movable electrode 6 having an electrode face 11 facing an electrode face 11 of the reference electrode 4 is formed on the upper end of the concave portion 8 and is fixed to both ends of the opening of the concave portion so that it stretches across the opening. A capacitor is formed by the movable electrode 6 and the reference electrode 4. Like the reference electrode 4, the movable electrode 6 a thin film is formed by means of aluminum deposition or the like.
FIG. 19 shows an equivalent circuit for this variable capacitor. In FIG. 19, a bias voltage source 18 is connected to a capacitor 19 formed by the reference electrode 4 and movable electrode 6 to apply a DC bias voltage thereto. This voltage is applied between terminal portions (not shown) leading from one end of each of the electrodes 4 and 6 to produce a potential difference between the electrodes 4 and 6.
As shown in FIG. 18 when the bias voltage source 18 applies the external bias voltage between the reference electrode 4 and movable electrode 6 to produce a potential difference between the electrodes 4 and 6, the movable electrode 6 is deflected toward the reference electrode 4 by the action of a Coulomb force (electrostatic force) to the position indicated in phantom FIG. 18. This results in a change in the electrode spacing (the gap) between the movable electrode 6 and reference electrode 4. As a result, there is provided a variable capacitor whose electrostatic capacity changes in accordance with the external bias voltage applied between the movable electrode 6 and reference electrode 4.
As shown in FIG. 19, a cut-off capacitor 16 is normally provided in a circuit using such a variable capacitor to eliminate DC components from the bias voltage source 18. For example, this prevents various circuits such as an oscillation circuit provided in the area 17 indicated by the broken line in FIG. 19 from being adversely affected by the DC components from the bias voltage source 18.
A variable capacitor according to this proposal is constituted by a single element. Therefore, it is advantageous in that it can be made small in size and fabricated simply unlike a conventional variable air capacitor which require complicated mechanisms such as a rotating mechanism for varying the electrostatic capacity (for example, by mechanically rotating a screw to increase and decrease the area in which the electrodes face each other). Further, unlike a varactor diode, there is no decrease in the Q-value due to an increase in the internal resistance introduced in an attempt to improve the withstand voltage. Thus, this capacitor is attracting much attention as an excellent variable capacitor having high withstand voltage and Q-value.
However, in a variable capacitor according to the above-described proposal, the displacement of the movable electrode 6 is limited by the relationship between the Coulomb force applied to the movable electrode 6 and the spring force produced in the movable electrode 6 when it is deflected by the Coulomb force. This has resulted in a problem in that it is not easy to increase the rate of the capacity change achieved by the deflection of the movable electrode 6.
The reason is that the above-described spring force and Coulomb force are not easily balanced when the amount of the displacement of the movable electrode 6 exceeds one-third of the distance between the reference electrode 4 and movable electrode 6.
A description will now be made on the relationship between the amount of the displacement of the movable electrode 6 and the Coulomb and spring forces exerted on the movable electrode 6. The movable electrode 6 will fix itself in a position where equilibrium is reached between the Coulomb force exerted on the movable electrode 6 due to the potential difference between the movable electrode 6 and reference electrode 4 on the one hand and the spring force of the moveable electrode 6 that tends to return the movable electrode 6 to the initial undeflected position when the movable electrode 6 is deflected by the Coulomb force on the other. This relationship is expressed by the following equation: EQU F=kx=1/2.multidot..epsilon.S{V/(x.sub.0 -x)}.sup.2 Equation 1
where k represents the spring constant of the movable electrode 6; S represents the area of the movable electrode 6 that faces the reference electrode 4; .epsilon. represents a dielectric constant; V represents the potential difference between the electrodes 4 and 6; x.sub.0 represents the distance between the electrodes 4 and 6; and x represents the amount of the displacement of the movable electrode 6. Equation 1 can be transformed into the following Equation 2 if we put u=x/x.sub.0 and K=.epsilon.S/2kx.sub.0.sup.3 : EQU u(1-u).sup.2 =KV.sup.2 Equation 2
The relationship as shown in FIG. 20 is derived from Equation 2 if we put u(1-u).sup.2 =f(u). The function f(u) is a cubic function wherein KV.sup.2 peaks at about 0.15 when u=1/3. FIG. 20 shows that the spring force and Coulomb force become unbalanced when the bias voltage V increases causing u to exceed 1/3. When this happens, the movable electrode 6 can contact the reference electrode 4. Although the spring force and Coulomb force can be balanced with u exceeding 1/3, some measures must be taken to control the bias voltage V depending on the spring force.
Therefore, the practical range of the displacement of the movable electrode 6 is limited to one-third the distance between the movable electrode 6 and reference electrode 4. This has limited the maximum capacity change rate of this variable capacitor to 50%, and it has not been possible to increase the varying rate further.